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Characters that cross dimensions have elicited an avid interest in literature and cinema. In analogy to these characters, we explore the concept of migration: Process by which an agent moves between embodiments, being active in only one at a time. We developed an autonomous artificial pet with two embodiments: A virtual within a smartphone and a physical robotic embodiment. Considering that owners' interactions with real pets lead to emotional attachment and potentially related health benefits, we conducted a user study with elementary school students to assess their attachment to the prototype and how natural they felt the interaction was. By the end of the experiment children felt closer to the artificial pet and 43.3% considered the two embodiments to correspond to the same entity, although migration was never explained to them. As a result, this paper presents a novel generic methodology that allows the evaluation of other implemented prototypes that support migration. Furthermore, we created a set of design guidelines for migrating agents.